I am staying in Cortina. I want to travel from Dobbiaco to Innsbruck. I also wan to train to St. Moritz. Advice?

I will be staying in Cortina, Italy for a week. I want to take the train from Dobbiaco to Innsbruck, Austria for a day trip. also I want to bus from Cortina to St. Moritz, Switzerland. spend the night there and return to Cortina for dinner the following night.

Thanks - Aileen